Position of high correlation using matlab

Question

I have a signal that more or less repeats itself (not exactly the same from one to the next, see plot to the left). If I use autocorrelation I get a number of maximums (right plot), but it doesn't tell me where (which sample number) the correlation is high. It gives me the lags but I lose information on the position, that is, the sample number in my original data where the signal occurs. For example in the auto-corr. plot, the second peak at sample 500 should correspond to the signal at about sample 750 in the data plot. I could do this by using a small window that moves over the data trace and find the maximums but it takes too much time. Is there a faster way of doing this in matlab? thanks.

Answer 1

I think you're misinterpreting autocorrelation. The correlation peak at 5000 is not due to a single location in the time series, but rather to the fact that the entire time series is similar to itself, when offset by 5000 samples. As much of that peak is due to the time series peak at 18000 as it is to the time series peak at 7500. Your autocorrelation will get very strange if, for example, you do not have a truly periodic time series (that is, if the interval between pulses is nonuniform).

If you can isolate one example of your pulse, and choose the location you want as your t=0, then a correlation of that one pulse with the time series will give you just what you want. Each pulse will light up clearly, at the time location at which it occurs. Then you just need a peak finder.

Answer 2

Yes, you could get the indices of the elements with the maximum amplitude using

treshold = max(a)/2
ind = find(a>=treshold)

where a is the matrix containing the correlation result.